A body moves over one fourth of a circular arc in a circle of radius r. The magnitude of distance travelled and displacement will be respectively.

To find the distance travelled and the magnitude of the displacement of a body moving over one-fourth of a circular arc, let us analyze the motion step-by-step.

1. Calculating the Distance Travelled:
The distance travelled by a body is the actual length of the path covered. For a complete circle of radius _r, the total perimeter (circumference) is:
$C=2\pi r$
Since the body covers one-fourth of the circular arc, the distance travelled (_s) is:
$s=\frac{1}{4}\times 2\pi r=\frac{\pi r}{2}$

2. Calculating the Magnitude of Displacement:
Displacement is the shortest straight-line distance between the initial position and the final position of the body.
Let the center of the circle be at the origin _{O(0, 0)}.
If the body starts at point _A on the x-axis, its coordinates are _{(r, 0)}.
After travelling one-fourth of the circle (an angle of 90 degrees or _π/2 radians), the body reaches point _B on the y-axis, with coordinates _{(0, r)}.
The straight-line distance between _A and _B forms the hypotenuse of a right-angled triangle _OAB, where the other two sides are the radii of the circle, both of length _r.
Using the Pythagorean theorem, the magnitude of the displacement (_d) is:
$d=\sqrt{r^2+r^2}=\sqrt{2r^2}=r\sqrt{2}$

Thus, the magnitude of the distance travelled is $\frac{\pi r}{2}$ and the magnitude of the displacement is $r\sqrt{2}$.

Therefore, the correct option is πr/2, r√2.